A086665 Difference between sum of divisors of n and integer log of n, i.e., A000203(n) - A001414(n).

1, 1, 1, 3, 1, 7, 1, 9, 7, 11, 1, 21, 1, 15, 16, 23, 1, 31, 1, 33, 22, 23, 1, 51, 21, 27, 31, 45, 1, 62, 1, 53, 34, 35, 36, 81, 1, 39, 40, 79, 1, 84, 1, 69, 67, 47, 1, 113, 43, 81, 52, 81, 1, 109, 56, 107, 58, 59, 1, 156, 1, 63, 91, 115, 66, 128, 1, 105, 70, 130, 1, 183, 1, 75, 111, 117, 78, 150, 1, 173, 109, 83

Offset: 1

Author

Jon Perry, Jul 27 2003

Keywords

• nonn

Examples

			a(10) = sigma(10) - (2 + 5) = 1 + 2 + 5 + 10 - 7 = 11.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000203, A001414, A075255, A374126, A374127.

Programs

Mathematica

sigma1 = Table[Plus @@ Divisors[n], {n, 100}]; sopfr = Prepend[ Array[ Plus @@ Map[ Times @@ #1 &, FactorInteger[ # ] ] &, 100, 2 ], 0 ]; Table[sigma1[[n]] - sopfr[[n]], {n, 100}] (* Alonso del Arte, Dec 01 2004 *)

PARI

sodf(n)=local(x); x=factor(n); sum(i=1,length(x[,1]),sum(j=1,x[i,2],x[i,1])); for(i=1,60,print1(sigma(i)-sodf(i)","))

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A086665(n) = (sigma(n)-A001414(n)); \\ Antti Karttunen, Jul 06 2024

Extensions

Data section extended up to a(82) by Antti Karttunen, Jul 06 2024